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Full-Text Articles in Algebraic Geometry
Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney
Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney
Mathematics Faculty Publications
We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices.
The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy
The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy
Mathematics Faculty Publications
We prove an implicit function theorem for non-commutative functions. We use this to show that if p ( X;Y ) is a generic non-commuting polynomial in two variables, and X is a generic matrix, then all solutions Y of p ( X;Y ) = 0 will commute with X
Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy
Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy
Mathematics Faculty Publications
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.